Ubuntu 14.04 LTS, in Amazon EC2. The following steps resolved this issue for me:
1. Edit server.xml and change port="8080" to "80"
sudo vi /var/lib/tomcat7/conf/server.xml
<Connector connectionTimeout="20000" port="8080" protocol="HTTP/1.1" redirectPort="8443"/>
2. Edit tomcat7 file (if the file is not created then you need to create it)
sudo vi /etc/default/tomcat7
uncomment and change #AUTHBIND=no to yes
3. Install authbind
sudo apt-get install authbind
4. Run the following commands to provide tomcat7 read+execute on port 80.
sudo touch /etc/authbind/byport/80
sudo chmod 500 /etc/authbind/byport/80
sudo chown tomcat7 /etc/authbind/byport/80
5. Restart tomcat:
sudo /etc/init.d/tomcat7 restart